GMAT Quantitative Review

3.0 Math Review

3.2 Algebra

8. Inequalities

An inequality is a statement that uses one of the following symbols:

image

Some examples of inequalities are imageimage, and image. Solving a linear inequality with one unknown is similar to solving an equation; the unknown is isolated on one side of the inequality. As in solving an equation, the same number can be added to or subtracted from both sides of the inequality, or both sides of an inequality can be multiplied or divided by a positive number without changing the truth of the inequality. However, multiplying or dividing an inequality by a negative number reverses the order of the inequality. For example, image, but image.

To solve the inequality image for x, isolate x by using the following steps:

image

To solve the inequality image for x, isolate x by using the following steps:

image